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Random Projection Trees Revisited

2020-01-06 | |  68 |   41 |   0

Abstract

The Random Projection Tree (RPT REE) structures proposed in [1] are space partitioning data structures that automatically adapt to various notions of intrinsic dimensionality of data. We prove new results for both the RPT REE -M AX and the RPT REE -M EAN data structures. Our result for RPT REE -M AX gives a nearoptimal bound on the number of levels required by this data structure to reduce the size of its cells by a factor s 图片.pngWe also prove a packing lemma for this data structure. Our final result shows that low-dimensional manifolds have bounded Local Covariance Dimension. As a consequence we show that RPT REE -M EAN adapts to manifold dimension as well.

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